The Cold war started because the United States was afraid of the spread of Communism and they got salty because Berlin was captured by the USSR at the end of ww2.
The Allies developed an early plan of fighting Communism called "Containment" which is where the U.S. would send weapons and equipment to countries with a Communist revolution brewing. This was the main tactic of fighting where we see containment being used, we see it in Greece in the late 40's, Korea in the 50's and Vietnam in the 60's and 70's. later in Afghanistan in the early 80's
Nuclear Weapons played a huge role as well, with the installation of MAD or "Mutually Assured Destruction" which was agreed upon by the US and USSR where if one launched nuclear weapons, so would the other, resulting in total nuclear apocalypse.
Propaganda was used by both nations in the form of putting the first man, rocket, woman, dog, and monkey in space, the Cuban Missile Crises, Beating the Americans in Hockey and Basketball, and capturing Berlin. for the Soviets and for the Americans it was The Space Race and putting a man on the moon.
Ultimately those were the big three, other weapons used were basic, tanks, planes and guns that were lent to nations of interest during wars.